In the classifier model depicted in Fig. REF , the input point cloud data is first decomposed into `\(L\) ' subsets via the cloning technique described in the previous section. Inside each subset, relations between each query point and its neighbours is sought by the KNN algorithm. This is done by applying four MLPs \(\lbrace 64,64,64,64\rbrace \)  to each cloning subset.
Similar to KNN-based networks [1]}, [2]}, [3]}, we compute K nearest neighbour responses of edges emanating from the enquiry feature point and stack them with the enquiry feature point.
The KNN algorithm is considerably affected by the density of points. If the 3D model is sparse, then the best K responses will lie within a large volume neighbourhood while such responses in a high density model may fall into a small radius [Fig. REF ].
Moreover, adjacent points in high density 3D samples would share similar KNN responses and this makes the network data-dependent. In other words, the network may fail to work for test point cloud data with different samplings from the training data.
This problem can be seen in almost all KNN-based networks which here is solved by the cloning layer.
In the proposed model, the LP layer finds the most repeated relations across different subsets and then labels them as stable patterns.
Even in the presence of changes in point coordinates, the patterns remain approximately unchanged as we consider overall behaviour of a group of points rather than the exact behaviour of each point.
